// Extend the Array class
//数组最大值
Array.prototype.max = function () {
  return Math.max.apply(null, this);
};
//数组最小值
Array.prototype.min = function () {
  return Math.min.apply(null, this);
};
//数组平均值
Array.prototype.mean = function () {
  var i, sum;
  for (i = 0, sum = 0; i < this.length; i++)
    sum += this[i];
  return sum / this.length;
};
//将数组第一项取出为v，生成长度为n的数组，每个数组item为v
Array.prototype.rep = function (n) {
  var arrayn = new Array(n);
  var v = this[0];
  for (var i = 0; i < n; i++) {
    arrayn[i] = v;
  }
  return arrayn;
};
Array.prototype.pip = function(x, y) {
  let i, j, c = false;
  for(i=0,j=this.length-1;i<this.length;j=i++) {
    if( ((this[i][1]>y) != (this[j][1]>y)) &&
      (x<(this[j][0]-this[i][0]) * (y-this[i][1]) / (this[j][1]-this[i][1]) + this[i][0]) ) {
      c = !c;
    }
  }
  return c;
}

let kriging = {};

// Matrix algebra
var kriging_matrix_diag = function(c, n) {
  let i, Z = [0].rep(n*n);
  for(i=0;i<n;i++) Z[i*n+i] = c;
  return Z;
};
var kriging_matrix_transpose = function(X, n, m) {
  let i, j, Z = Array(m*n);
  for(i=0;i<n;i++)
    for(j=0;j<m;j++)
      Z[j*n+i] = X[i*m+j];
  return Z;
};
var kriging_matrix_scale = function(X, c, n, m) {
  let i, j;
  for(i=0;i<n;i++)
    for(j=0;j<m;j++)
      X[i*m+j] *= c;
};
var kriging_matrix_add = function(X, Y, n, m) {
  let i, j, Z = Array(n*m);
  for(i=0;i<n;i++)
    for(j=0;j<m;j++)
      Z[i*m+j] = X[i*m+j] + Y[i*m+j];
  return Z;
};
// Naive matrix multiplication
var kriging_matrix_multiply = function(X, Y, n, m, p) {
  let i, j, k, Z = Array(n*p);
  for(i=0;i<n;i++) {
    for(j=0;j<p;j++) {
      Z[i*p+j] = 0;
      for(k=0;k<m;k++)
        Z[i*p+j] += X[i*m+k]*Y[k*p+j];
    }
  }
  return Z;
};
// Cholesky decomposition
var kriging_matrix_chol = function(X, n) {
  let i, j, k, sum, p = Array(n);
  for(i=0;i<n;i++) p[i] = X[i*n+i];
  for(i=0;i<n;i++) {
    for(j=0;j<i;j++)
      p[i] -= X[i*n+j]*X[i*n+j];
    if(p[i]<=0) return false;
    p[i] = Math.sqrt(p[i]);
    for(j=i+1;j<n;j++) {
      for(k=0;k<i;k++)
        X[j*n+i] -= X[j*n+k]*X[i*n+k];
      X[j*n+i] /= p[i];
    }
  }
  for(i=0;i<n;i++) X[i*n+i] = p[i];
  return true;
};
// Inversion of cholesky decomposition
var kriging_matrix_chol2inv = function(X, n) {
  let i, j, k, sum;
  for(i=0;i<n;i++) {
    X[i*n+i] = 1/X[i*n+i];
    for(j=i+1;j<n;j++) {
      sum = 0;
      for(k=i;k<j;k++)
        sum -= X[j*n+k]*X[k*n+i];
      X[j*n+i] = sum/X[j*n+j];
    }
  }
  for(i=0;i<n;i++)
    for(j=i+1;j<n;j++)
      X[i*n+j] = 0;
  for(i=0;i<n;i++) {
    X[i*n+i] *= X[i*n+i];
    for(k=i+1;k<n;k++)
      X[i*n+i] += X[k*n+i]*X[k*n+i];
    for(j=i+1;j<n;j++)
      for(k=j;k<n;k++)
        X[i*n+j] += X[k*n+i]*X[k*n+j];
  }
  for(i=0;i<n;i++)
    for(j=0;j<i;j++)
      X[i*n+j] = X[j*n+i];

};
// Inversion via gauss-jordan elimination
var kriging_matrix_solve = function(X, n) {
  let m = n;
  let b = Array(n*n);
  let indxc = Array(n);
  let indxr = Array(n);
  let ipiv = Array(n);
  let i, icol, irow, j, k, l, ll;
  let big, dum, pivinv, temp;

  for(i=0;i<n;i++)
    for(j=0;j<n;j++) {
      if(i==j) b[i*n+j] = 1;
      else b[i*n+j] = 0;
    }
  for(j=0;j<n;j++) ipiv[j] = 0;
  for(i=0;i<n;i++) {
    big = 0;
    for(j=0;j<n;j++) {
      if(ipiv[j]!=1) {
        for(k=0;k<n;k++) {
          if(ipiv[k]==0) {
            if(Math.abs(X[j*n+k])>=big) {
              big = Math.abs(X[j*n+k]);
              irow = j;
              icol = k;
            }
          }
        }
      }
    }
    ++(ipiv[icol]);

    if(irow!=icol) {
      for(l=0;l<n;l++) {
        temp = X[irow*n+l];
        X[irow*n+l] = X[icol*n+l];
        X[icol*n+l] = temp;
      }
      for(l=0;l<m;l++) {
        temp = b[irow*n+l];
        b[irow*n+l] = b[icol*n+l];
        b[icol*n+l] = temp;
      }
    }
    indxr[i] = irow;
    indxc[i] = icol;

    if(X[icol*n+icol]==0) return false; // Singular

    pivinv = 1 / X[icol*n+icol];
    X[icol*n+icol] = 1;
    for(l=0;l<n;l++) X[icol*n+l] *= pivinv;
    for(l=0;l<m;l++) b[icol*n+l] *= pivinv;

    for(ll=0;ll<n;ll++) {
      if(ll!=icol) {
        dum = X[ll*n+icol];
        X[ll*n+icol] = 0;
        for(l=0;l<n;l++) X[ll*n+l] -= X[icol*n+l]*dum;
        for(l=0;l<m;l++) b[ll*n+l] -= b[icol*n+l]*dum;
      }
    }
  }
  for(l=(n-1);l>=0;l--)
    if(indxr[l]!=indxc[l]) {
      for(k=0;k<n;k++) {
        temp = X[k*n+indxr[l]];
        X[k*n+indxr[l]] = X[k*n+indxc[l]];
        X[k*n+indxc[l]] = temp;
      }
    }

  return true;
}

// Variogram models
var kriging_variogram_gaussian = function(h, nugget, range, sill, A) {
  return nugget + ((sill-nugget)/range)*
    ( 1.0 - Math.exp(-(1.0/A)*Math.pow(h/range, 2)) );
};
var kriging_variogram_exponential = function(h, nugget, range, sill, A) {
  return nugget + ((sill-nugget)/range)*
    ( 1.0 - Math.exp(-(1.0/A) * (h/range)) );
};
var kriging_variogram_spherical = function(h, nugget, range, sill, A) {
  if(h>range) return nugget + (sill-nugget)/range;
  return nugget + ((sill-nugget)/range)*
    ( 1.5*(h/range) - 0.5*Math.pow(h/range, 3) );
};

// Train using gaussian processes with bayesian priors
kriging.train = function(t, x, y, model, sigma2, alpha) {
  let variogram = {
    t      : t,
    x      : x,
    y      : y,
    nugget : 0.0,
    range  : 0.0,
    sill   : 0.0,
    A      : 1/3,
    n      : 0
  };
  switch(model) {
    case "gaussian":
      variogram.model = kriging_variogram_gaussian;
      break;
    case "exponential":
      variogram.model = kriging_variogram_exponential;
      break;
    case "spherical":
      variogram.model = kriging_variogram_spherical;
      break;
  };

  // Lag distance/semivariance
  let i, j, k, l, n = t.length;
  let distance = Array((n*n-n)/2);
  for(i=0,k=0;i<n;i++)
    for(j=0;j<i;j++,k++) {
      distance[k] = Array(2);
      distance[k][0] = Math.pow(
        Math.pow(x[i]-x[j], 2)+
        Math.pow(y[i]-y[j], 2), 0.5);
      distance[k][1] = Math.abs(t[i]-t[j]);
    }
  distance.sort(function(a, b) { return a[0] - b[0]; });
  variogram.range = distance[(n*n-n)/2-1][0];

  // Bin lag distance
  let lags = ((n*n-n)/2)>30?30:(n*n-n)/2;
  let tolerance = variogram.range/lags;
  let lag = [0].rep(lags);
  let semi = [0].rep(lags);
  if(lags<30) {
    for(l=0;l<lags;l++) {
      lag[l] = distance[l][0];
      semi[l] = distance[l][1];
    }
  }
  else {
    for(i=0,j=0,k=0,l=0;i<lags&&j<((n*n-n)/2);i++,k=0) {
      while( distance[j][0]<=((i+1)*tolerance) ) {
        lag[l] += distance[j][0];
        semi[l] += distance[j][1];
        j++;k++;
        if(j>=((n*n-n)/2)) break;
      }
      if(k>0) {
        lag[l] /= k;
        semi[l] /= k;
        l++;
      }
    }
    if(l<2) return variogram; // Error: Not enough points
  }

  // Feature transformation
  n = l;
  variogram.range = lag[n-1]-lag[0];
  let X = [1].rep(2*n);
  let Y = Array(n);
  let A = variogram.A;
  for(i=0;i<n;i++) {
    switch(model) {
      case "gaussian":
        X[i*2+1] = 1.0-Math.exp(-(1.0/A)*Math.pow(lag[i]/variogram.range, 2));
        break;
      case "exponential":
        X[i*2+1] = 1.0-Math.exp(-(1.0/A)*lag[i]/variogram.range);
        break;
      case "spherical":
        X[i*2+1] = 1.5*(lag[i]/variogram.range)-
          0.5*Math.pow(lag[i]/variogram.range, 3);
        break;
    };
    Y[i] = semi[i];
  }

  // Least squares
  let Xt = kriging_matrix_transpose(X, n, 2);
  let Z = kriging_matrix_multiply(Xt, X, 2, n, 2);
  Z = kriging_matrix_add(Z, kriging_matrix_diag(1/alpha, 2), 2, 2);
  let cloneZ = Z.slice(0);
  if(kriging_matrix_chol(Z, 2))
    kriging_matrix_chol2inv(Z, 2);
  else {
    kriging_matrix_solve(cloneZ, 2);
    Z = cloneZ;
  }
  let W = kriging_matrix_multiply(kriging_matrix_multiply(Z, Xt, 2, 2, n), Y, 2, n, 1);

  // Variogram parameters
  variogram.nugget = W[0];
  variogram.sill = W[1]*variogram.range+variogram.nugget;
  variogram.n = x.length;

  // Gram matrix with prior
  n = x.length;
  let K = Array(n*n);
  for(i=0;i<n;i++) {
    for(j=0;j<i;j++) {
      K[i*n+j] = variogram.model(Math.pow(Math.pow(x[i]-x[j], 2)+
        Math.pow(y[i]-y[j], 2), 0.5),
        variogram.nugget,
        variogram.range,
        variogram.sill,
        variogram.A);
      K[j*n+i] = K[i*n+j];
    }
    K[i*n+i] = variogram.model(0, variogram.nugget,
      variogram.range,
      variogram.sill,
      variogram.A);
  }

  // Inverse penalized Gram matrix projected to target vector
  let C = kriging_matrix_add(K, kriging_matrix_diag(sigma2, n), n, n);
  let cloneC = C.slice(0);
  if(kriging_matrix_chol(C, n))
    kriging_matrix_chol2inv(C, n);
  else {
    kriging_matrix_solve(cloneC, n);
    C = cloneC;
  }

  // Copy unprojected inverted matrix as K
  var K_C = C.slice(0);
  let M = kriging_matrix_multiply(C, t, n, n, 1);
  variogram.K = K_C;
  variogram.M = M;

  return variogram;
};

// Model prediction
kriging.predict = function(x, y, variogram) {
  let i, k = Array(variogram.n);
  for(i=0;i<variogram.n;i++)
    k[i] = variogram.model(Math.pow(Math.pow(x-variogram.x[i], 2)+
      Math.pow(y-variogram.y[i], 2), 0.5),
      variogram.nugget, variogram.range,
      variogram.sill, variogram.A);
  return kriging_matrix_multiply(k, variogram.M, 1, variogram.n, 1)[0];
};
kriging.variance = function(x, y, variogram) {
  let i, k = Array(variogram.n);
  for(i=0;i<variogram.n;i++)
    k[i] = variogram.model(Math.pow(Math.pow(x-variogram.x[i], 2)+
      Math.pow(y-variogram.y[i], 2), 0.5),
      variogram.nugget, variogram.range,
      variogram.sill, variogram.A);
  return variogram.model(0, variogram.nugget, variogram.range,
    variogram.sill, variogram.A)+
    kriging_matrix_multiply(kriging_matrix_multiply(k, variogram.K,
      1, variogram.n, variogram.n),
      k, 1, variogram.n, 1)[0];
};

// Gridded matrices or contour paths
//OpenLayers鐨刾olygon锛歰l.geom.Polygon(coordinates, opt_layout)
kriging.grid = function(polygons, variogram, width) {
  let i, j, k, n = polygons.length;
  if(n==0) return;

  // Boundaries of polygons space
  let xlim = [polygons[0][0][0], polygons[0][0][0]];
  let ylim = [polygons[0][0][1], polygons[0][0][1]];
  for(i=0;i<n;i++) // Polygons
    for(j=0;j<polygons[i].length;j++) { // Vertices
      if(polygons[i][j][0]<xlim[0])
        xlim[0] = polygons[i][j][0];
      if(polygons[i][j][0]>xlim[1])
        xlim[1] = polygons[i][j][0];
      if(polygons[i][j][1]<ylim[0])
        ylim[0] = polygons[i][j][1];
      if(polygons[i][j][1]>ylim[1])
        ylim[1] = polygons[i][j][1];
    }
  // Alloc for O(n^2) space
  let xtarget, ytarget;
  let a = Array(2), b = Array(2);
  let lxlim = Array(2); // Local dimensions
  let lylim = Array(2); // Local dimensions
  let x = Math.ceil((xlim[1]-xlim[0])/width);//x鏂瑰悜涓婄殑鏍煎瓙鏁�
  let y = Math.ceil((ylim[1]-ylim[0])/width);//y鏂瑰悜涓婄殑鏍煎瓙鏁�

  let A = Array(x+1);
  for(i=0;i<=x;i++) A[i] = Array(y+1);//A鏄竴涓簩缁寸煩闃�
  for(i=0;i<n;i++) {
    // Range for polygons[i]
    lxlim[0] = polygons[i][0][0];
    lxlim[1] = lxlim[0];
    lylim[0] = polygons[i][0][1];
    lylim[1] = lylim[0];
    for(j=1;j<polygons[i].length;j++) { // Vertices
      if(polygons[i][j][0]<lxlim[0])
        lxlim[0] = polygons[i][j][0];
      if(polygons[i][j][0]>lxlim[1])
        lxlim[1] = polygons[i][j][0];
      if(polygons[i][j][1]<lylim[0])
        lylim[0] = polygons[i][j][1];
      if(polygons[i][j][1]>lylim[1])
        lylim[1] = polygons[i][j][1];
    }

    // Loop through polygon subspace
    a[0] = Math.floor(((lxlim[0]-((lxlim[0]-xlim[0])%width)) - xlim[0])/width);
    a[1] = Math.ceil(((lxlim[1]-((lxlim[1]-xlim[1])%width)) - xlim[0])/width);
    b[0] = Math.floor(((lylim[0]-((lylim[0]-ylim[0])%width)) - ylim[0])/width);
    b[1] = Math.ceil(((lylim[1]-((lylim[1]-ylim[1])%width)) - ylim[0])/width);
    for(j=a[0];j<=a[1];j++)
      for(k=b[0];k<=b[1];k++) {
        xtarget = xlim[0] + j*width;
        ytarget = ylim[0] + k*width;
        if(polygons[i].pip(xtarget, ytarget))
          A[j][k] = kriging.predict(xtarget,
            ytarget,
            variogram);
      }
  }
  A.xlim = xlim;
  A.ylim = ylim;
  A.zlim = [variogram.t.min(), variogram.t.max()];
  A.width = width;
  return A;
};
kriging.contour = function(value, polygons, variogram) {
  return null;
};

// Plotting on the DOM
kriging.plot = function(canvas, grid, xlim, ylim, colors) {
  // Clear screen
  let ctx = canvas.getContext("2d");
  ctx.clearRect(0, 0, canvas.width, canvas.height);

  // Starting boundaries
  let range = [xlim[1]-xlim[0], ylim[1]-ylim[0], grid.zlim[1]-grid.zlim[0]];
  let i, j, x, y, z;
  let n = grid.length;
  let m = grid[0].length;
  let wx = Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));
  let wy = Math.ceil(grid.width*canvas.height/(ylim[1]-ylim[0]));
  for(i=0;i<n;i++)
    for(j=0;j<m;j++) {
      if(grid[i][j]==undefined) continue;
      x = canvas.width*(i*grid.width+grid.xlim[0]-xlim[0])/range[0];
      y = canvas.height*(1-(j*grid.width+grid.ylim[0]-ylim[0])/range[1]);
      z = (grid[i][j]-grid.zlim[0])/range[2];
      if(z<0.0) z = 0.0;
      if(z>1.0) z = 1.0;

      ctx.fillStyle = colors[Math.floor((colors.length-1)*z)];
      ctx.fillRect(Math.round(x-wx/2), Math.round(y-wy/2), wx, wy);
    }
};

kriging.plot_rainbow = function(canvas, grid, xlim, ylim, rainbow) {
  // Clear screen
  let ctx = canvas.getContext("2d");
  ctx.clearRect(0, 0, canvas.width, canvas.height);

  // Starting boundaries
  let range = [xlim[1]-xlim[0], ylim[1]-ylim[0], grid.zlim[1]-grid.zlim[0]];
  let i, j, x, y, z;
  let n = grid.length;
  let m = grid[0].length;
  let wx = Math.ceil(grid.width*canvas.width/(xlim[1]-xlim[0]));
  let wy = Math.ceil(grid.width*canvas.height/(ylim[1]-ylim[0]));
  for(i=0;i<n;i++)
    for(j=0;j<m;j++) {
      if(grid[i][j]==undefined) continue;
      x = canvas.width*(i*grid.width+grid.xlim[0]-xlim[0])/range[0];
      y = canvas.height*(1-(j*grid.width+grid.ylim[0]-ylim[0])/range[1]);
      z = (grid[i][j]-grid.zlim[0])/range[2];
      if(z<0.0) z = 0.0;
      if(z>1.0) z = 1.0;

      ctx.fillStyle ='#'+ rainbow.colourAt(z);
      ctx.fillRect(Math.round(x-wx/2), Math.round(y-wy/2), wx, wy);
    }
};

export default kriging;

/*
eg.
 var variogram = K.kriging.train(values, lngs, lats, model, sigma2, alpha);
 var grid = K.kriging.grid(_polygons, variogram, width);
 K.kriging.plot(this.canvas, grid, [extent.xmin, extent.xmax], [extent.ymin, extent.ymax], colors);
*/
